The isotope abundance calculator computes average atomic mass from isotope masses and their natural abundances using a weighted average. It also solves the reverse problem: given the average atomic mass and one isotope's abundance in a two-isotope system, find the unknown abundance. Essential for AP Chemistry and general chemistry mass spectrometry problems.
Isotope 1
Isotope 2 (unknown abundance)
Presets:
Results
Average Atomic Mass
amu
Unknown Abundance (Isotope 2)
%
Isotope Abundance
Calculation Steps
| Isotope | Mass (amu) | Abundance | Contribution |
|---|
How to Use the Isotope Abundance Calculator
The isotope abundance calculator uses the weighted average formula to find average atomic mass from isotope data — or runs it in reverse to find an unknown isotope abundance. This covers one of the most common problem types in AP Chemistry and general chemistry mass spectrometry units.
Mode 1: Calculate Average Atomic Mass
Enter the exact isotope masses (in amu) and natural abundances (in %) for each isotope. The average atomic mass = Σ(abundance × mass) for all isotopes, where abundance is expressed as a decimal fraction. For chlorine with two isotopes (Cl-35 and Cl-37), the calculation gives 35.45 amu — the value you see on the periodic table.
Mode 2: Find Unknown Abundance
If a two-isotope system has a known average atomic mass but one unknown abundance, enter the known average mass, both isotope masses, and the known abundance of isotope 1. Since abundances must sum to 100%, isotope 2's abundance = 100% − abundance₁. The calculator verifies this is consistent with the given average mass.
Worked Example: Chlorine
Chlorine has two stable isotopes: Cl-35 (mass = 34.969 amu, abundance = 75.76%) and Cl-37 (mass = 36.966 amu, abundance = 24.24%).
- Contribution from Cl-35: 0.7576 × 34.969 = 26.496 amu
- Contribution from Cl-37: 0.2424 × 36.966 = 8.960 amu
- Average atomic mass: 26.496 + 8.960 = 35.456 amu ≈ 35.45 amu (periodic table value)
About Isotope Masses
Isotope masses (exact atomic masses) differ slightly from their mass numbers due to nuclear binding energy — this is called the mass defect. Carbon-12 is exactly 12.000000 amu by definition (it's the reference standard). Other isotopes' masses are measured relative to this standard using mass spectrometry. The calculator uses the NIST-recommended exact masses for the built-in presets.
FAQ
What is average atomic mass?
Average atomic mass (also called standard atomic weight) is the weighted average of all naturally occurring isotope masses of an element, weighted by their natural abundances. It reflects the actual isotopic composition of naturally occurring samples, which is why carbon has an atomic mass of 12.011 rather than exactly 12.
Is this calculator free?
Yes, completely free with no signup or account required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally in your browser. No data is sent to any server.
What is the difference between mass number and isotope mass?
The mass number is the total count of protons plus neutrons (an integer, e.g., 12 for C-12). The isotope mass is the actual measured mass in atomic mass units (amu), which is slightly different due to nuclear binding energy — C-12 is exactly 12.000 by definition, but C-13 is 13.00335 amu.
Why do isotope abundances have to add up to 100%?
The abundances represent fractions of all naturally occurring atoms of that element. Together they must account for 100% of the atoms. If you enter values that don't sum to 100%, the calculator will normalize them and note the discrepancy.
How do I find unknown isotope abundance?
Switch to Mode 2 (Find Unknown Abundance). For a two-isotope system, if you know the average atomic mass and one isotope's abundance, the other is simply 100% minus the first. Enter the known abundance of isotope 1, and the calculator solves for isotope 2's abundance using the formula: avg mass = x₁m₁ + (1-x₁)m₂.